The present invention relates to a new and distinct cultivar of Isotoma, which is grown as an ornamental annual bedding plant for use in the garden and landscape and in planted containers. The new cultivar is known botanically as Isotoma axillaris, and will be referred to hereinafter by the cultivar name ‘TMLU 1301’. The genus Isotoma is occasionally known by the alternate name Laurentia. 
During the 1990s, the inventor's employer had commenced in Ipswich, Essex, United Kingdom a seed breeding program in the genus Isotoma from which no cultivars were selected or introduced. In 2010, the inventor commenced a breeding program to develop named cultivars of Isotoma with the objectives of large flower size and novel flower colors. The inventor was able to utilize seeds and seedlings from the previous seed breeding program. The present invention is a result of the inventor's desire to develop a large flowered deep purple variety of Isotoma. 
In 2010, the inventor carried out controlled pollination of the following seedlings. For the male parent, the inventor used a seedling raised as ‘LU11022’ (unreleased and unpatented) which exhibits very large deep pink flowers. For the female parent, the inventor used a seedling raised as ‘LU11039’ (unreleased and unpatented) which exhibited large violet-blue flowers. Within the offspring of this pollination, coded as ‘LU12009’, one plant in particular impressed the inventor for its naturally prolific basal and lateral branching and its very large glowing vibrant purple flowers. This plant was selected and was subsequently named ‘TMLU 1301’.
‘TMLU 1301’ was first asexually propagated by the inventor in 2013 in Ipswich, Suffolk, United Kingdom. Asexual propagation was accomplished using tip cuttings. Since that time, under careful observation, the distinguishing characteristics of ‘TMLU 1301’ have been determined stable and uniform, and to reproduce true to type in successive generations of asexual propagation.